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 A318359 a(1) = 4; for n > 1, a(n) is the least positive number not yet in the sequence such that Sum_{k=1..n} a(k) divides Sum_{k=1..n} a(k)^3. 2
 4, 1, 5, 8, 9, 12, 6, 20, 10, 3, 39, 65, 52, 11, 7, 42, 147, 441, 294, 366, 222, 35, 514, 257, 1285, 771, 3084, 672, 99, 925, 608, 291, 2061, 229, 495, 140, 81, 288, 12088, 1511, 750, 476, 209, 2603, 752, 7645, 1079, 5816, 2210, 2830, 1996, 1162, 328, 3690 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Is this sequence infinite? For any v > 0, let b_v be the variant of this sequence starting with v: - b_4 = a (this sequence), - b_1 = A000027 (and indeed, A000217(n) divides A000537(n) for any n > 0), - for v in {1, 2, 3, 5}: b_v(n) = n for all n > 0 except a finite number. This sequence is a variant of A318358. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..500 EXAMPLE For n = 3: - (4^3 + 1^3 + 2^3) == 3 mod (4 + 1 + 2), - (4^3 + 1^3 + 3^3) == 4 mod (4 + 1 + 3), - (4^3 + 1^3 + 5^3) == 0 mod (4 + 1 + 5), - hence a(3) = 5. PROG (PARI) s=0; s3=0; p=0; v=4; for (n=1, 54, print1 (v ", "); s+=v; s3+=v^3; p+=2^v; for (w=1, oo, if (!bittest(p, w) && (s3+w^3)%(s+w)==0, v=w; break))) CROSSREFS Cf. A000027, A000217, A000537, A318358. Sequence in context: A011443 A016687 A139356 * A209297 A243525 A300071 Adjacent sequences:  A318356 A318357 A318358 * A318360 A318361 A318362 KEYWORD nonn AUTHOR Rémy Sigrist, Aug 24 2018 STATUS approved

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)